Pls help!!!! Due today

The constant of proportionality relating the number of miles y to the number of minutes x is 1/6.

To find the constant of proportionality, we can use the formula: y = kx. Where y represents the number of miles run, x represents the time taken in minutes, and k is the constant of proportionality. Coach Liba ran 9 miles in 54 minutes. We can use these values to solve for k: 9 = k(54)

Dividing both sides by 54, we get: k = 9/54 = 1/6. This means that for every 1 minute Coach Liba runs, he covers 1/6th of a mile. Or for every 6 minutes, he covers 1 mile.

The ratio of the number of miles run to the time taken in minutes is constant and equal to 1/6. This can help us predict how far Coach Liba will run in a given amount of time or how long it will take him to run a certain distance.

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The area of Vanessa's patio is represented by the expression 3x⁴ - 4x³ - 13x² + 35x + 10, which is obtained by multiplying the expressions representing the length and width.

To find the area of Vanessa's patio, we need to multiply the expressions representing the length and width.

Length = 3x² + 5x + 10

Width = x² - 3x - 1

Area = Length x Width

Area = (3x² + 5x + 10)(x² - 3x - 1)

To multiply these expressions, we can use the distributive property and then simplify

Area = 3x⁴ - 4x³ - 13x² + 35x + 10

Therefore, the expression that represents the area of Vanessa's patio is 3x⁴ - 4x³ - 13x² + 35x + 10.

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The required circumference of the circle with a diameter of 97 cm is 304 cm.

The circumference of a circle can be calculated using the formula:

C = πd

Where 'd' is the diameter of the circle, and 'π' is a mathematical constant approximately equal to 3.14159.

In this case, the diameter of the circle is given as 97 cm. So we can substitute this value into the formula to get:

C = πd

C = π(97 cm)

C ≈ 304.35 cm

Rounding this answer to 3 significant figures gives:

C ≈ 304 cm

Therefore, the circumference of the circle with a diameter of 97 cm is 304 cm.

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Answer:

V =base area × height or [(3√3)/2]a2h

where

a = base length

h = height of the prism

Step-by-step explanation:

The formula to calculate the future value of an investment with compound interest is:

A = P(1 + r/n)^(n*t)

where:

A = future value

P = principal (initial investment)

r = annual interest rate (as a decimal)

n = number of times interest is compounded per year

t = time (in years)

In this case, we have:

P = $200 (initial investment)

r = 20% = 0.20

n = 1 (compounded annually)

t = 6 (6 years)

So, we can plug these values into the formula:

A = 200(1 + 0.20/1)^(1*6)

A = 200(1.20)^6

A = $766.97 (rounded to the nearest cent)

Therefore, Robert will have approximately $766.97 in his retirement account after 6 years.

The time it takes the ball to hit the ground is 0.375 seconds.

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.

To calculate the amount of time it takes the ball to hit the ground, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for t

Hence, the time is 0.375 seconds.

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Each child, Miriam, Joe, and Paul, received one-sixth (1/6) of the entire cake.

To determine what part of the entire cake each child got, we need to divide the one-half of a cake that Stanley has equally among his three children, Miriam, Joe, and Paul.

The result is (1/6), which means that each child, Miriam, Joe, and Paul, received one-sixth (1/6) of the entire cake.

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The environmental agency should sample at least 746 vehicles.

In order to determine how many cars should be sampled for a full investigation, we can use the formula for sample size:
n = (Z^2 * p * q) / E^2
where:
- n = sample size
- Z = the Z-score for the desired level of confidence (in this case, 1.645 for 90% confidence)
- p = the proportion of cars in the population with faulty emissions systems (which we can estimate as 12/60 = 0.2 based on the initial sample)
- q = 1 - p
- E = the desired margin of error (2% in this case, or 0.02)
Plugging in these values, we get:
n = (1.645^2 * 0.2 * 0.8) / 0.02^2
n ≈ 746
Therefore, the environmental agency should sample at least 746 vehicles for a full investigation in order to estimate the percentage of cars violating clean air emissions standards with a margin of error of 2% and 90% confidence.

Hence  ,To estimate the percentage of cars violating clean air emissions standards with a margin of error of 2% and 90% confidence, the environmental agency should sample at least 746 vehicles for a full investigation.

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Answer:

-----------------------

Given:

The difference is the amount of decrease:

Find the percentage decrease:

Therefore, the price of the car has been reduced by 17%.

The price of the car has been decreased by  of 17% percentage.

To find the percentage decrease of the price of the car

Calculate the difference between the original price and the reduced price

Divide difference by the original price, and then multiply by 100 to convert it to a percentage:

Percentage decrease = (reduction in price / original price) x 100%

The reduction in price is:

$17,500 - $14,525 = $2,975

The original price is:

$17,500

So the percentage decrease is:

(2975 / 17500) x 100% = 17%

Therefore, the price of the car has been decreased by 17%.

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In case of a helicopter and is flying at 160 miles per hour at a constant altitude above a straight road, the speed of the car is equals to the -197.57 mph.

There is a helicopter which is flying at 160 miles per hour at a constant altitude of 0.75 miles above a straight road. During this radar is used to determine the distance of oncoming car is exactly 1 mile from helicopter. Distance decreasing rate = 130 miles per hour

Here, we want to calculate the speed of the car. Using geometry, there is formed a right angled triangle, see above figure. Let the length of base, height and hypothenuse be x,y and z respectively. The distance from the helicopter to the car, represents hypotenuse, say z. The hypotenuse of the triangle is decreasing at 66 mph, i.e. dz/dt = -130mph

From Pythagoras theorem, z² = x² + y²

differentiating wrt time, [tex]2z \frac{dz}{dt} = 2x \frac{dx}{dt} + 2y \frac{dy}{dt}[/tex]

we know, dy/dt is zero since copter never changes height. Also since y = 0.75 miles and z = 1 mile, [tex] x = \sqrt{1²-0.75²} [/tex]

= 0.658 miles

As we know speed is rate of change of position, so speed of car is dx/dt. Now, Substitute all known values in above formula, 2 mi × 1 × -130 mph = 2× 0.658 m dx/dt + 2×0

=> dx/dt = - 130/0.658

= -197.57 mph

Hence, required value is - 197.57 mph.

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The class interval containing the median speed is 30 < s < 40.

We must first establish the median position before we can locate the class interval holding the median speed.

By dividing the overall frequency by two, the median position can be calculated.

Total frequency = 12 + 16 + 18 + 2 + 2 = 50

Median position = 50 / 2 = 25

Now, we have to solve for the class interval that has the median position which is the 25th value.

20 < s < 30: Frequency is 12, cumulative frequency is 12 (Not containing the 25th value)

30 < s < 40: Frequency is 16, cumulative frequency is 12 + 16 = 28 (Contains the 25th value)

So, the class interval containing the median speed is 30 < s < 40.

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The area of the tray is approximately 28.26 square inches.

To find the area of the tray, we need to use the formula for the area of a circle, which is:

Area = π x radius²

Here, π (pronounced "pi") is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. Its approximate value is 3.14.

In our case, the radius of the tray is given as 3 inches. So, we can substitute this value into the formula and calculate the area as follows:

Area = π x 3²

= 3.14 x 9

= 28.26 square inches

This means that if we were to cover the tray completely with paint or any other material, it would require 28.26 square inches of that material.

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Answer:

15.10 ft to nearest hundredth.

Step-by-step explanation:

We have 2 right triangles one within the other

For the larger triangle

tan 43 = h / 65    where h is the total height to the top of steeple from ground

h = 65 tan 43

For small triangle

tan 35 = h2 / 65   where h2 is the hoght of the bottom of steeple from the ground

h2 = 65 tan 35

So height of the steeple

= h - h2

= 65 tan43 - 65 tan35

= 15.099 feet.

If Porter's family ordered 3 pizzas and they ate 1 pizza, then they are left with 2 pizzas.

None of the given options is correct.

Given information:

Porter's family ordered 3 pizzas. They ate 1 of the pizzas.

Since the question is asking for the amount of pizza left, the answer can be evaluated by subtraction operation:

Mathematical operations like subtraction exist.

It is employed to delete words or objects from the phrase.

As per the above concept, apply in the situation,

3 pizzas - 1 pizza = 2 pizzas.

Therefore, the correct answer is not listed among the options provided.

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Answer: F,B,D

Hope this helps : )

Step-by-step explanation:

Answer:

B, C, F

Step-by-step explanation:

B, C, and F are the only correct statements

Draw the 2 triangles, correctly labeled, and compare them.  This makes it easy to visualize which choices are true vs. false.

The key features of this exponential function include the following:

y-intercept of f: (0, 10).

y-intercept of g: (0, 5).

Domain of both f and g: All real numbers or (-∞, ∞).

Range of both f and g = (0, ∞) or {y|y ≥ 0}.

End behavior of both f and g: as x → -∞, y → 0 and x → ∞, y → ∞

In Mathematics and Geometry, an exponential function is typically represented by the following mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the given exponential function f, we can logically deduce that the y-intercept is represented by a, which is equal to 10 while the y-intercept of g is equal to 5.

In conclusion, there is a horizontal asymptote at y = 0 because it is a line which the graph of a given function approaches, but never touches or crosses.

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Answer:

0.436 ≠ 0.064

Step-by-step explanation:

P(A and B)=P(A) x P(B)

0.436 = 0.4 x 0.16

0.436 ≠ 0.064

If Adam wants to play video games he will have to finish homework, clean the dishwasher, and clean the room so the time he spends in total is 148 minutes by arithmetic all the timings respectively.

To find the total time Adam spent doing homework and cleaning before playing video games,

we add the time he spent on each task: 48 minutes for homework + 25 minutes for cleaning out the dishwasher + 75 minutes for cleaning his room = 148 minutes.

Therefore, Adam had to spend 148 minutes doing homework and cleaning before playing video games.

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The question is -

Adam wanted to play his video games. His mother told him that he needed to finish his homework, clean out the dishwasher, and clean his room before playing video games. He completed his homework in 48 minutes. He took 25 minutes to clean out the dishwasher. He took 75 minutes to clean his room. How much time did Adam have to spend doing homework and cleaning before playing video games?

Answer: B

Explanation:

A + B = (2x - 7x² + 3) + (4x² - 12x) = 2x - 7x² + 3 + 4x² - 12x = -3x² -10x + 3

a) The appropriate sample size to achieve a margin of error of $0.10 with a confidence level of 91.5% is 111

b) The appropriate sample size to achieve a margin of error of $0.07 with a confidence level of 95.845% is 301

c) The appropriate sample size to achieve a margin of error of $0.05 with a confidence level of 97.268% is 543 integer).

a) To achieve a margin of error of $0.10 with a confidence level of 91.5%, the appropriate sample size can be calculated as follows:

Margin of error (E) = z* (standard deviation/√(n))

where z* is the z-value associated with the desired confidence level, and n is the sample size.

We can rearrange the formula to solve for n:

n = [(z* * standard deviation) / E]²

Substituting the given values:

z* = 1.70 (from the z-table for 91.5% confidence level)

Standard deviation = $0.25

E = $0.10

n = [(1.70 * 0.25) / 0.10]² = 110.25 ≈ 111 (rounding up to the nearest integer).

b) To achieve a margin of error of $0.07 with a confidence level of 95.845%, the appropriate sample size can be calculated as follows:

z* = 1.99 (from the z-table for 95.845% confidence level)

Standard deviation = $0.25

E = $0.07

n = [(1.99 * 0.25) / 0.07]² = 300.06 ≈ 300 (rounding up to the nearest integer).

c) To achieve a margin of error of $0.05 with a confidence level of 97.268%, the appropriate sample size can be calculated as follows:

z* = 2.34 (from the z-table for 97.268% confidence level)

Standard deviation = $0.25

E = $0.05

n = [(2.34 * 0.25) / 0.05]² = 542.52 ≈ 543 (rounding up to the nearest integer).

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The negative change in the y value will shift the graph downwards.

When a graph of a figure or a point get a negative change in its y value it gets shifted downwards.

When, f(x) - a is f(x) shifted downward a units.

Ex. Shift 3 units down,

Before

y = x² +x, Point (x, y)

After

y = x² +x -3, Point (x, y-3)

Hence, the negative change in the y value will shift the graph downwards.

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a.  A statistical test used to help answer the question of whether an observed difference is real or just due to chance error- true

The statistical test referred to in the question is known as a hypothesis test. It is used to determine the probability that the observed difference between two groups or variables is not due to chance but rather represents a true difference. The test involves setting up a null hypothesis, which assumes that there is no difference between the groups or variables, and an alternative hypothesis, which assumes that there is a real difference.

The test calculates a p-value, which represents the probability of obtaining the observed difference by chance if the null hypothesis is true.

If the p-value is below a predetermined level of significance (usually 0.05), then the null hypothesis is rejected and the alternative hypothesis is accepted.

This means that the observed difference is considered real and not just due to chance error.

Hence, If the p-value is below a certain level of significance, the null hypothesis is rejected and the alternative hypothesis is accepted, indicating that the observed difference is real.

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The probability that a randomly selected student is interested in a "spinning-room" and also that they are a "graduate-student" is 0.428.

The total number of students that are surveyed is = 500 students,

Out of the 500 students surveyed, 41 are interested in a spinning room and are in year 1-2,

⇒ 75 are interested and are in year 3-4, and

⇒ 87 are interested and are graduate students.

So, the total number of students interested in a spinning room is

⇒ 41 + 75 + 87 = 203,

Out of these 203 students interested in a spinning room, 87 are graduate students.

So, probability that randomly selected student is interested in "spinning-room" and is a "graduate-student" is :

⇒ P(spinning room and graduate student) = 87/203,

⇒ P(spinning room and graduate student) = 0.428,

Therefore, the required probability is 0.428.

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The given question is incomplete, the complete question is

A university recently surveyed 500 students to determine which new fitness area to offer in its recreation facility. the results of the survey are summarized in the following table.

                              Spinning Room   Climbing Wall     Ellipticals

Year 1-2                              41                     81                         25

Year 3-4                             75                    78                         44

Graduate Student             87                     49                        20

What is the probability that a randomly selected student is interested in a spinning room and that they are a graduate student?

The equation of the ellipse is given by  ( x - 2 )² / 25 + ( y - 2 )² / 16 = 1

Given data ,

Let the center of the ellipse be ( h , k ) = ( 2 , 2 )

Now , the length of the major axis is 2a = 10 units

The length of the minor axis 2b = 8 units

So , a = 5 and b = 4

Now , the standard for of equation of ellipse is

( x²/a² ) + ( y²/b² ) = 1

On simplifying , we get

( x - 2 )² / ( 5 )² + ( y - 2 )² / ( 4 )² = 1

( x - 2 )² / 25 + ( y - 2 )² / 16 = 1

Hence , the equation of ellipse is ( x - 2 )² / 25 + ( y - 2 )² / 16 = 1

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Answer:

x = (-3 + sqrt(23)i) / 2 and x = (-3 - sqrt(23)i) / 2.

Step-by-step explanation:

To solve the quadratic equation -x^2 + 3x - 8 = 0, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = -1, b = 3, and c = -8. Substituting into the quadratic formula, we get:

x = (-3 ± sqrt(3^2 - 4(-1)(-8))) / 2(-1)

Simplifying the expression inside the square root:

x = (-3 ± sqrt(9 - 32)) / (-2)

x = (-3 ± sqrt(-23)) / (-2)

Since the square root of a negative number is not a real number, the solutions to this quadratic equation are complex numbers. We can simplify the expression by writing the solutions in terms of the imaginary unit i:

x = (-3 ± sqrt(23)i) / 2

Therefore, the solutions to the quadratic equation -x^2 + 3x - 8 = 0 are x = (-3 + sqrt(23)i) / 2 and x = (-3 - sqrt(23)i) / 2.

Answer:

Step-by-step explanation:630

Answer:

[tex]{ \boxed{ \mathfrak{amswer}}} :{ \underline{ \tt{ \: { \alpha }^{2} + { \beta }^{2} = - 1} \: }}[/tex]

Step-by-step explanation:

From General equation of a polynomial:

✍️ x² - (Sum of roots)x + (Product of roots) = 0

Therefore;

[tex]{ \tt{f(x) = {x}^{2} - x + 1 = 0 }}[/tex]

From the equation,

[tex]{ \tt{ \alpha + \beta = 1}} - - - { \rm{sum}} \\ { \tt{ \alpha \beta = 1 }} - - - { \rm{product}}[/tex]

From the question:

[tex]{ \tt{ {( \alpha + \beta )}^{2} = ( \alpha + \beta )( \alpha + \beta ) }} \\ \\ { \tt{ {( \alpha + \beta )}^{2} = { \alpha }^{2} + 2 \alpha \beta + { \beta }^{2} }} \\ \\ { \tt{ {( \alpha + \beta )}^{2} = ( { \alpha }^{2} + { \beta }^{2} ) + 2 \alpha \beta }} \\ \\ { \boxed{ \tt{( { \alpha }^{2} + { \beta }^{2} ) = {{( \alpha + \beta )}^{2} - 2 \alpha \beta }}}}[/tex]

Therefore, from sum and product

[tex]{ \tt{ { \alpha }^{2} + { \beta }^{2} = (1) {}^{2} - 2(1) }} \\ = { \tt{1 - 2}} \\ = - 1[/tex]

Answer:

Slope of green line:

[tex]m = \frac{ - 3 - 3}{4 - ( - 4))} = - \frac{6}{8} = - \frac{3}{4} [/tex]

Slope of red line:

[tex]m = \frac{3 - ( - 5)}{3 - ( - 3)} = \frac{8}{6} = \frac{4}{3} [/tex]

The slopes of these two lines are negative reciprocals of each other.

Therefore, the correct answer is True (A).